If `af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2)` is equal to (a) `(2a)/(2(a^2-b^2))` (b) `a/(a^2-b^2)` (c)`(a+2b)/(a^2-b^2)` (d) none of these

If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then a^2-b^2 is equal to (a) 1/(a^2e^2) (b) a^2e^2 (c) b^2e^2 (d) none of these

If a x^2+2h x y+b y^2=1,t h e n(d^2y)/(dx^2) is (a) (h^2-a b)/((h x+b y)^2) (b) (a b-h^2)/((h x+b y)^2) (h^2+a b)/((h x+b y)^2) (d) none of these

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these

If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)^2) (b) (a b-h^2)/((h x+b y)^2) (h^2+a b)/((h x+b y)^2) (d) none of these

If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)^2) (b) (a b-h^2)/((h x+b y)^2) (h^2+a b)/((h x+b y)^2) (d) none of these

If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then a^2-b^2 is equal to (A) 1/(a^2e^2) (B) a^2e^2 (C) b^2e^2 (D) none of these

If f(1)=2, f\'(x)=f(x) and h(x)=fof(x) then h'\(1) is equal to (A) 4e (B) 2e^2 (C) 4e^2 (D) e^2

if for nonzero x , af(x) + bf(1/x) =1/x-5 , where a!=b then f(2) =

Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such that A=B X , then X is equal to (a) 1/2[(2, 4), (3, -5)] (b) 1/2[(-2, 4), (3, 5)] (c) [(2, 4), (3,-5)] (d) none of these

If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a^2+c^2=-a b b. a^2-c^2=-a b c. a^2-c^2=a b d. none of these